Hyperplane Assisted Evolutionary Algorithm for Many-Objective Optimization Problems

In many-objective optimization problems (MaOPs), forming sound tradeoffs between convergence and diversity for the environmental selection of evolutionary algorithms is a laborious task. In particular, strengthening the selection pressure of population toward the Pareto-optimal front becomes more challenging, since the proportion of nondominated solutions in the population scales up sharply with the increase of the number of objectives. To address these issues, this paper first defines the nondominated solutions exhibiting evident tendencies toward the Pareto-optimal front as prominent solutions, using the hyperplane formed by their neighboring solutions, to further distinguish among nondominated solutions. Then, a novel environmental selection strategy is proposed with two criteria in mind: 1) if the number of nondominated solutions is larger than the population size, all the prominent solutions are first identified to strengthen the selection pressure. Subsequently, a part of the other nondominated solutions are selected to balance convergence and diversity and 2) otherwise, all the nondominated solutions are selected; then a part of the dominated solutions are selected according to the predefined reference vectors. Moreover, based on the definition of prominent solutions and the new selection strategy, we propose a hyperplane assisted evolutionary algorithm, referred here as hpaEA, for solving MaOPs. To demonstrate the performance of hpaEA, extensive experiments are conducted to compare it with five state-of-the-art many-objective evolutionary algorithms on 36 many-objective benchmark instances. The experimental results show the superiority of hpaEA which significantly outperforms the compared algorithms on 20 out of 36 benchmark instances.